We established a Dengue fever transmission model that considered spatial heterogeneity and the advective effect of wind by using the theories of monotonic homogeneity and  chain transitive sets. The results  show that the basic reproduction number R₀ determines the global threshold dynamics of the model: when R₀≤1, the disease goes extinct;  when R₀, the disease persists. Numerical analysis results show  that R₀ varies non-monotonically with the advection rate, and  increasing the density of alternative hosts is helpful for disease prevention and control.

We discussed a class of  inverse problem of  time fractional order diffusion equations by using the fractional order Tikhonov regularization method. We gave selection criteria for the regularization parameter under  prior and posterior conditions, and gave rigorous  proofs of the convergence of the method. Numerical experimental results show that  the fractional order Tikhonov regularization method is effective in solving this problem.

Based on a nonlinear demand function, we established a  fishery economic model with  multi-agent  completely uncooperative, and discussed the local stability and multi-stability of the system, as well as the influence of related parameters on the local and global dynamics of the system. The  results show that it will help multiple participants obtain better returns when the cost parameters and the price elasticity are small, but  the market demand is large, and the intrinsic growth rate can be effectively controlled within a certain range.

We established an optimization model for the refractive index inversion problem in the terrain parabolic equation based on  the framework of optimal control theory. Firstly, through rigorous mathematical analysis, we proved the existence of minimum value  for the objective functional and its necessary conditions. Secondly, we proved  the local uniqueness and stability of the minimum value to the problem.

We considered the existence of weak solutions to  elliptic coupled systems with p-Laplace operators and Hardy type singular terms in the whole space R^N. New criteria for the existence of at least one and at least two weak solutions were established by using  variational methods combined with  critical point theorems when the sign-changing nonlinearities satisfied suitable hypotheses.

We investigated the global structure of positive radial solutions for a class of quasilinear elliptic boundary value problems with Dirichlet boundary conditions based on  bifurcation theory. Specifically, by introducing two critical exponents f₀ and f_∞,  under two typical cases of  f₀∈(0,∞), f_∞=0 and f₀=∞, f_∞=0, we prove the existence of unbounded connected branches emanating from bifurcation points, which utimately asymptotically extend to infinity along the λ-axis.

We considered a stochastic SEIQR monkeypox epidemic model with  Gaussian white noise. Firstly, the existence and uniqueness of the global positive solution for the stochastic model were proved by using stopping time theory. By constructing a Lyapunov function and combining it with  Ito formula, the asymptotic behavior of the solutions of stochastic model near the disease-free equilibrium point and endemic equilibrium point of the corresponding deterministic model was given. Secondly, we gave conditions for the average persistence of the solutions and disease extinction of the stochastic model. Finally, numerical simulations were conducted to examine the impact of noise on the model. The results show  that the stochastic model perturbs near the equilibrium point of the deterministic model, and  the degree of perturbation is  positively correlated with  the noise intensity. When the noise is sufficiently large, the disease will become extinct.

Let R be an associative ring with identity, V and W be classes of left R-modules, and Y be classes of right R-modules. Firstly, we define (V,W,Y)-Gorenstein flat modules, and give an equivalent characterization of (V,W,Y)-Gorenstein flat modules. Secondly, we  prove that this class is closed with respect to  direct sums, direct summands and kernels of epimorphisms under certain conditions.

By using edge-moving operations and the Perron-Frobenius theorem, we discussed the problem of the spectral radius of the complement distance  of tree graph.  We determined the unique trees with maximum  and minimum spectral radii of  the complementary distance, respectively, and  determined the graph with the minimum spectral radius of  the  complementary distance in the complementary graph of the tree,  as well as the graph with  the i-th largest spectral radius of complementary distance, where  i=1,2,…,(n-2)/2.

By using graph transformation method, we determined the largest total Mostar index for n-order cactus graph G with k cycles, 
and characterized the corresponding extremal graphs, when 2n+k>18 and n≥3k+1,  Mo_t(G)≤2n²+3nk-6n-25k+k²+4, and its equal sign holds if and only if G is the graph composed of attaching k end-blocks of length 4 and (n-3k-1) pendant edges to a common vertex. Furthermore, by discussing the classification of  the remaining cactus graph, we obtained the second-largest total Mostar index and characterized the corresponding extremal graphs.

Aiming at the problem of sparse covariance matrix estimation, we proposed a sparse covariance matrix estimator based on the MCP (minimax concave penalty) penalized log-likelihood, and solved it by using  the coordinate descent algorithm. The simulation results show that the proposed method can achieve  smaller L₁ norms, Kullback-Leibler distances, and Frobenius norms compared to the Lasso penalty and SCAD (smoothly clipped absolute deviation) penalty methods when estimating sparse covariance matrices in most cases, especially under the AR(1) model setting, the performance is more outstanding. In addition, the superior performance of the MCP penalty method for practical applications is verified by analyzing the protein concentration data measured by flow cytometry.

Aiming at the quality and efficiency problems caused by insufficient utilization of multilayer relations in large-scale group decision-making, we proposed  a group consensus decision-making method based on multilayer network structure detection. The method  modelled multilayer relations of decision-makers as distinguishable coupled organizations, developed  an interactive restart random walk algorithm to map opinion propagation, detected community structure and influence distribution, and optimized detection efficiency by using nearest neighbor approximation incremental computing. The calculation  examples and simulation results verify that it can strengthen the leading role of decision-makers with strong influence, reduce conflicts, achieve the balance between high consensus and efficient computing, and provide an effective approach for group decision-making in complex coupled environments.

Aiming at  the impact of factors such as  occlusion, pose variations and lighting on facial expression recognition, we proposed a facial expression recognition method based on local correlation and multi-scale spatial attention. Firstly, through the local correlation module, local features were combined with global features to enhance the connections between local features, thereby improving recognition performance of the model in complex environments. Secondly,  the multi-scale spatial attention mechanism was adopted to extract and fuse spatial structural information at different levels, enhancing the robustness of the model.  Experimental results show that the proposed method demonstrates superior facial expression recognition performance on the RAF-DB and AffectNet datasets, validating its effectiveness and generalization ability.

Aiming at the problem of low tracking accuracy in trajectory tracking control of 5-degree of freedom (DOF) parallel mechanisms caused by model uncertainties, external disturbances, and input saturation, we proposed a discrete integral sliding mode control algorithm with time-varying disturbance compensation considering input saturation. Firstly, to address the problem of input saturation,  while considering the limitations of  input assignment and input rate of change, we designed a discrete saturation compensation auxiliary system to  eliminate the input saturation characteristics. Secondly, we designed a time-varying disturbance compensation discrete integral sliding mode controller to  achieve real-time compensation for lumped disturbances, thereby reducing system steady-state error while suppressing chattering. Finally, through simulation experiments, a comparative analysis was conducted between the proposed method and the disturbance compensation discrete sliding mode control algorithm, 
considering both with and without input saturation. The experimental results show that the proposed algorithm outperforms the comparative algorithms in terms of control accuracy and saturation constraints, and can effectively achieve high-precision trajectory tracking control of parallel mechanisms considering both lumped disturbances and input saturation, with high engineering application value.

Aiming at  the problem of minimizing latency and energy consumption in service migration in dynamic Internet of Vehicles, we proposed a service migration strategy based on graph neural networks. Firstly, we established a system model to model the service migration problem as a multi-objective optimization problem that minimized latency and energy consumption. Secondly, we  transformed the problem into a Markov decision process, and defined the states, actions, and reward functions. Finally, a graph convolutional neural network was used  to extract features from edge network topology and node information, and combining  task information to propose a deep reinforcement learning task migration decision algorithm based on graph convolutional neural networks to make service migration decisions. Simulation experiment results show that the proposed algorithm outperforms other baseline algorithms in reducing average task latency and energy consumption, and can provide an effective solution for efficient, low consumption, and stable service migration in the environment of Internet of Vehicles.

We studied the initial-boundary value problem of a class of non-Newtonian fluids with initial vacuum and linear damping. Under the condition that the initial energy was small and the initial value met certain compatibility, we used the technique of weighted energy estimation and Zlotnik inequality to overcome the nonlinearity of the viscous term of the momentum equation, and proved that the density function had a uniform upper bound of time. Furthermore, we adopted the continuity method to obtain the existence and uniqueness conclusion of the global strong solution of the initial-boundary value problem of non-Newtonian fluid.

Under humid conditions, we prepared polycaprolactone (PCL) ordered photonic films by using solvent evaporation self-assembly method. We obtained highly ordered porous through films by controlling the solution concentration. We used ion sputtering method to adsorb a layer of metal on the surface of the through films, and replaced silver ammonia solution with silver. The results show that this silver-coated ordered porous through film has a double-layer ordered porous structure, and its conductivity is significantly enhanced. Compared with the single-layer film, the light transmittance of the double-layer film is limited by the incident angle and can achieve the function of directional light transmission. The properties of the heat-treated photonic films change, exhibiting high-temperature resistance and enhanced light transmittance at all angles. This directional light transmission ordered array film has the characteristics of electromagnetic shielding.

Aiming at the problem of the low sensitivity, poor portability and easy influence by environmental temperature of glucose sensors based on biological enzymes, we developed and designed a high sensitivity flexible glucose sensor, and  prepared flexible glucose sensors with Au electrodes based on polyimide (PI) by using the screen-printing technique. We doped reduced graphene oxide (rGO) to improve electrode conductivity and enhance sensor sensitivity when preparing the glucose oxidase mixed solution. Additionally, we designed a portable detection system that could achieve in situ detection and temperature compensation correction through data processing, thereby reducing the impact of temperature on bioenzyme activity and enabling them to work normally at different environmental temperatures. The experimental results show that the glucose sensor has a detection sensitivity of 58.9 μA/(mmol·cm²) within 0—1.2 mmol/L, a detection limit of 5 μmol/L, and exhibits good selectivity, making it suitable for monitoring glucose concentration in human sweat.

We studied the effects of doping with four types of atoms, S,N,P,Si, as well as the adsorption of seven small molecules, NO,,NO₂,NH₃,CO,CO_2,SO₂ and H₂S on the geometric structure and electronic properties of two-dimensional B₄C₃ materials. The results show that compared with the intrinsic B₄C₃ material with bandgap of 2.020 eV, the bandgap width of both doped and small molecule adsorption systems is reduced. The bandgap value of the N-doped system is the smallest among the four systems, indicating that doping N atoms has the most significant effect on the electronic properties of B₄C₃. After NO₂ adsorption, B₄C₃ changes from semiconductor to metal, indicating that B₄C₃ can effectively detect NO₂ gas.

We prepared magnesium hydroxide by using the ammonia bubbling method. When the temperature ranged from 303.15 K to 353.15 K, we measured the solubility of magnesium chloride in different concentrations of ammonium chloride aqueous solution and deuterium volume fractions of 1.65×10^-4，1.30×10^-4，7.0×10^-5 water and ordinary water. We correlated the solubility data by using Apelblat equation and empirical equation, and calculated the solubility entropy, enthalpy, and standard Gibbs free energy change of magnesium chloride in ammonium chloride aqueous solution by using the modified Van’t-Hoff equation. The results show that under the same solvent conditions, the solubility of magnesium chloride increases with increasing temperature. Under the same temperature conditions, the solubility of magnesium chloride increases sequentially in ammonium chloride solution, ordinary water, and low deuterium water. The higher the concentration of ammonium chloride, the lower the solubility, and the lower the deuterium content, the higher the solubility. The Apelblat equation and empirical equation both show good correlation results, with a total relative error of 0.66%. The entropy change is the main factor affecting the dissolution process of magnesium chloride.

Using enzymatic lignin as raw material, porous lignin based carbon materials were constructed by optimizing the KOH activation process. The effects of parameters such as  carbon-alkali ratio,  activation temperature and activation time on the structure of lignin-|based porous carbon materials were studied   by using a one-step activation method. We tested the electrochemical properties of the prepared materials in a three-electrode system and assembled symmetrical supercapacitors by using KOH as the electrolyte to test the cycling stability of the material during continuous charge and discharge processes. The results show that  when the  activation temperature is 700 ℃,  the carbon-alkali ratio is 4∶1,  and the activation time is 2 h,  a porous carbon sample (ELC_700-2-4) with a high specific surface area (3 067 m²/g) and high microporosity (62.18%) can be prepared. In the three-electrode system,  the material exhibits excellent electrochemical performance in KOH as the electrolyte,  and the specific capacitance can reach 443 F/g at 1 A/g. The specific capacitance of ELC_700-2-4 electrode is 250 F/g at 1 A/g,  and the capacitance retention rate after 10 000 cycles is 95.55%,  indicating that the electrode has excellent cycling stability during continuous charging and discharging. The energy density of symmetrical capacitor is  8.6 W.h/kg when the power density is 500.16 W/kg. 

Aiming at the problem of the widespread presence of antibiotics such as sulfamethoxazole （SMX） in water bodies, which posed a threat to the ecosystem and human health, and were difficult to effectively remove by using conventional wastewater treatment processes，  we prepared a few-layer carbon nitride catalyst (Ni@C₃N₄) loaded with single-atom nickel,  which could efficiently electrocatalytically degrade sulfamethoxazole by generating hydrogen peroxide (H₂O₂) via an oxygen reduction reaction (ORR). Structural characterization show that nickel is highly dispersed in the few-layer carbon nitride matrix in the form of single-atoms and significantly modulates the electronic structure of the few-layer carbon nitride to optimize the active site distribution. Electrochemical test results show that Ni@C₃N₄ has excellent two-electron selectivity and rapid reaction kinetics. Under acidic conditions (pH=3), Ni@C₃N₄ can generate H₂O₂ via the two-electron pathway,  and degradation rate of sulfamethoxazole can reach 81.3% within 120 min, which is significantly better than that of the undoped carbon nitride catalyst. Kinetic analysis results show that the degradation process conforms to a pseudo-first-order reaction model. The research results provide new ideas for the treatment of antibiotics in water bodies.